中文名: 有限群的表示論與結合代數
原名: Representation Theory of Finite Groups and Associative Algebras
作者: Charles W. Curtis and Irving Reiner
資源格式: DJVU
版本: 清晰版
出版社: American Mathematical Society
書號: 0821840665
發行時間: 2006年
地區: 美國
語言: 英文
簡介:

內容簡介:
本書概述了有限群，結合環及結合代數表示論。除了Burnside書中表示論的經典內容，本書著重敘述了誘導特征，誘導表示，擬Frobenius環，Frobenius代數，整數表示及模表示論.迄今為止。其中的許多內容僅見於研究論文中。本書注重一般方法，將理論構建於滿足極小條件環上的模。為幫助研究者得到特定群的具體表示，書中包含了大量的例子以及問題，並給出了一些群表示應用於有限群結構理論的例子。
本書前三章給出了一些介紹性的材料,同時也為後續的章節提供了背景.
4-7章介紹了滿足極小條件的半單環的結構理論及其在群表示與特征上的應用
4,8,9,10章介紹了滿足極小條件的環及有限維代數
3,11章介紹了代數數論及群的整數表示
12章介紹了模表示論
First published in 1962, this classic book remains a remarkably complete introduction to various aspects of the representation theory of finite groups. One of its main advantages is that the authors went far beyond the standard elementary representation theory, including a masterly treatment of topics such as general non-commutative algebras, Frobenius algebras, representations over non-algebraically closed fields and fields of non-zero characteristic, and integral representations. These and many other subjects are treated extremely thoroughly, starting with basic definitions and results and proceeding to many important and crucial developments. Numerous examples and exercises help the reader of this unsurpassed book to master this important area of mathematics.
內容截圖:

目錄:
Notation
I.Background from Group Theory
II.Representations and Modules
III.Algebraic Number Theory
IV.Semi-simple Rings and Group Algebras
V.Group Characters
VI.Induced Characters
VII.Induced Representations
VIII.Non-Semi-Simple Rings
IX.Frobenius Algebras
X.Splitting Fields and Separable Algebras
XI.Integral Representations
XII.Modular Representations
Index